This may sound a little silly, but what's the point of picking up the VOL power up other than obviously increasing the volume? And why would I want to increase the volume anyway?
The VOL powerup boosts the overall volume of the song. This sounds obvious, but the non-obvious part is that the louder the song is, the stronger your ship is. Quieter songs (and songs that let the beat.... mmmm... drop!?) can put you in situations where you can't effectively attack. VOL powerups boost the effect of the music on your ship throughout the song, which can help smooth out some of these issues.
Also, when your VOL and POW bars are maxed, you go into Beat Hazard mode, which grants a major boost to your damage output.